In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...

Yeast vacuole fusion involves three transmembrane SNAREs and a unique soluble SNARE, Vam7p. This SNARE cycles between vacuolar membrane-bound and cytosolic state. In its membrane-bound state, it is able to participate in vacuolar fusion by...

In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...

In this thesis we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...